By Christopher Monckton of Brenchley
I propose to raise a question about the Earth’s energy budget that has perplexed me for some years. Since further evidence in relation to my long-standing question is to hand, it is worth asking for answers from the expert community at WUWT.
A.E. Housman, in his immortal parody of the elegiac bromides often perpetrated by the choruses in the stage-plays of classical Greece, gives this line as an example:
I only ask because I want to know.
This sentiment is not as fatuous as it seems at first blush. Another chorus might say:
I ask because I want to make a point.
I begin by saying:
You say I aim to score a point. Not so:
I only ask because I want to know.
Last time I raised the question, in another blog, more heat than light was generated because the proprietrix had erroneously assumed that T / 4F, a differential essential to my argument, was too simple to be a correct form of the first derivative ΔT / ΔF of the fundamental equation (1) of radiative transfer:
, | Stefan-Boltzmann equation (1)
where F is radiative flux density in W m–2, ε is emissivity constant at unity, the Stefan-Boltzmann constant σ is 5.67 x 10–8 W m–2 K–4, and T is temperature in Kelvin. To avert similar misunderstandings (which I have found to be widespread), here is a demonstration that T / 4F, simple though it be, is indeed the first derivative ΔT / ΔF of Eq. (1):
. (2)
Like any budget, the Earth’s energy budget is supposed to balance. If there is an imbalance, a change in mean temperature will restore equilibrium.
My question relates to one of many curious features of the following energy-budget diagrams for the Earth:
Energy budget diagrams from (top left to bottom right) Kiehl & Trenberth (1997), Trenberth et al. (2008), IPCC (2013), Stephens et al. (2012), and NASA (2015).
Now for the curiosity:
“Consensus”: surface radiation FS falls on the interval [390, 398] W m–2.
There is a “consensus” that the radiative flux density leaving the Earth’s surface is 390-398 W m–2. The “consensus” would not be so happy if it saw the implications.
When I first saw FS = 390 W m–2 in Kiehl & Trenberth (1997), I deduced it was derived from observed global mean surface temperature 288 K using Eq. (1), assuming surface emissivity εS = 1. Similarly, TS = 289.5 K gives 398 W m–2.
The surface flux density cannot be reliably measured. So did the “consensus” use Eq. (1) to reach the flux densities shown in the five diagrams? Yes. Kiehl & Trenberth (1997) wrote: “Emission from the surface is assumed to follow Planck’s function, assuming a surface emissivity of 1.” Planck’s function gives flux density at a particular wavelength. Eq. (1) integrates that function across all wavelengths.
Here (at last) is my question. Does not the use of Eq. (1) to determine the relationship between TS and FS at the surface necessarily imply that the Planck climate-sensitivity parameter λ0,S applicable to the surface (where the coefficient 7/6 ballparks allowance for the Hölder inequality) is given by
= 0.215 K W–1 m2 ? (3)
The implications for climate sensitivity are profound. For the official method of determining λ0 is to apply Eq. (1) to the characteristic-emission altitude (~300 mb), where incoming and outgoing radiative fluxes are by definition equal, so that Eq. (4) gives incoming and hence outgoing radiative flux FE:
= 239.4 W m–2 (4)
where FE is the product of the ratio πr2/4πr2 of the surface area of the disk the Earth presents to the Sun to that of the rotating sphere; total solar irradiance S = 1366 W m–2; and (1 – α), where α = 0.3 is the Earth’s albedo. Then, from (1), mean effective temperature TE at the characteristic emission altitude is given by Eq. (5):
= 254.8 K. (5)
The characteristic emission altitude is ~5 km above ground level. Since mean surface temperature is 288 K and the mean tropospheric lapse rate is ~6.5 K km–1, Earth’s effective radiating temperature TE = 288 – 5(6.5) = 255 K, in agreement with Eq. (5). The Planck parameter λ0,E at that altitude is then given by (6):
= 0.310 K W–1 m2. (6)
Equilibrium climate sensitivity to a CO2 doubling is given by (7):
, (7)
where the numerator of the fraction is the CO2 radiative forcing, and f = 1.5 is the IPCC’s current best estimate of the temperature-feedback sum to equilibrium.
Where λ0,E = 0.313, equilibrium climate sensitivity is 2.2 K, down from the 3.3 K in IPCC (2007) because IPCC (2013) cut the feedback sum f from 2 to 1.5 W m–2 K–1 (though it did not reveal that climate sensitivity must then fall by a third).
However, if Eq. (1) is applied at the surface, the value λ0,S of the Planck sensitivity parameter is 0.215 (Eq. 3), and equilibrium climate sensitivity falls to only 1.2 K.
If f is no greater than zero, as a growing body of papers finds (see e.g. Lindzen & Choi, 2009, 2011; Spencer & Braswell, 2010, 2011), climate sensitivity falls again to just 0.8 K.
If f is net-negative, sensitivity falls still further. Monckton of Brenchley, 2015 (click “Most Read Articles” at www.scibull.com) suggest that the thermostasis of the climate over the past 810,000 years and the incompatibility of high net-positive feedback with the Bode system-gain relation indicate a net-negative feedback sum on the interval –0.64 [–1.60, +0.32] W m–2 K–1. In that event, applying Eq. (1) at the surface gives climate sensitivity on the interval 0.7 [0.6, 0.9] K.
Two conclusions are possible. Either one ought not to use Eq. (1) at the surface, reserving it for the characteristic emission altitude, in which event the value for surface flux density FS may well be incorrect and no one has any idea of what the Earth’s energy budget is, and still less of an idea whether there is any surface “radiative imbalance” at all, or the flux density at the Earth’s surface is correctly determined from observed global mean surface temperature by Eq. (1), as all five sources cited above determined it, in which event sensitivity is harmlessly low even under the IPCC’s current assumption of strongly net-positive temperature feedbacks.
Table 1 summarizes the effect on equilibrium climate sensitivity of assuming that Eq. (1) defines the relationship between global mean surface temperature TS and mean outgoing surface radiative flux density FS.
| Climate sensitivities to a CO2 doubling | |||||
| Source | Altitude | λ0 | f | ΔTS,100 | ΔTS,∞ |
| AR5 (2013) upper bound | 300 mb | 0.310 K W–1 m2 | +2.40 W m–2 K–1 | 2.3 K | 4.5 K |
| AR4 (2007) central estimate | 300 mb | 0.310 K W–1 m2 | +2.05 W m–2 K–1 | 1.6 K | 3.3 K |
| AR5 implicit central estimate | 300 mb | 0.310 K W–1 m2 | +1.50 W m–2 K–1 | 1.1 K | 2.2 K |
| AR5 lower bound | 300 mb | 0.310 K W–1 m2 | +0.75 W m–2 K–1 | 0.8 K | 1.5 K |
| M of B (2015) upper bound | 300 mb | 0.310 K W–1 m2 | +0.32 W m–2 K–1 | 0.7 K | 1.3 K |
| AR5 central estimate | 1013 mb | 0.215 K W–1 m2 | +1.50 W m–2 K–1 | 0.6 K | 1.2 K |
| M of B central estimate | 300 mb | 0.310 K W–1 m2 | –0.64 W m–2 K–1 | 0.5 K | 1.0 K |
| M of B upper bound | 1013 mb | 0.215 K W–1 m2 | +0.32 W m–2 K–1 | 0.5 K | 0.9 K |
| M of B lower bound | 300 mb | 0.310 K W–1 m2 | –1.60 W m–2 K–1 | 0.4 K | 0.8 K |
| M of B central estimate | 1013 mb | 0.215 K W–1 m2 | –0.64 W m–2 K–1 | 0.4 K | 0.7 K |
| Lindzen & Choi (2011) | 300 mb | 0.310 K W–1 m2 | –1.80 W m–2 K–1 | 0.4 K | 0.7 K |
| Spencer & Braswell (2011) | 300 mb | 0.310 K W–1 m2 | –1.80 W m–2 K–1 | 0.4 K | 0.7 K |
| M of B lower bound | 1013 mb | 0.215 K W–1 m2 | –1.60 W m–2 K–1 | 0.3 K | 0.6 K |
Table 1. 100-year (ΔTS,100) and equilibrium (ΔTS,∞) climate sensitivities to a doubling of CO2 concentration, applying Eq. (1) at the characteristic-emission altitude (300 mb) and, boldfaced, at the surface (1013 mb).
It is worth noting that, even before taking any account of the “consensus’” use of Eq. (1) to govern the relationship between TS and FS, the reduction in the feedback sum f between IPCC’s 2007 and 2013 assessment reports mandates a corresponding reduction in its central estimate of climate sensitivity from 3.3 to 2.2 K, of which only half, or about 1 K, would be expected to occur within a century of a CO2 doubling. The remainder would make itself slowly and harmlessly manifest over the next 1000-3000 years (Solomon et al., 2009).
Given that the Great Pause has endured for 18 years 6 months, the probability that there is no global warming in the pipeline as a result of our past sins of emission is increasing (Monckton of Brenchley et al., 2013). All warming that was likely to occur from emissions to date has already made itself manifest. Therefore, perhaps we start with a clean slate. Professor Murry Salby has estimated that, after the exhaustion of all affordably recoverable fossil fuels at the end of the present century, an increase of no more than 50% on today’s CO2 concentration – from 0.4 to 0.6 mmol mol–1 – will have been achieved.
In that event, replace Table 1 with Table 2:
| Climate sensitivities to a 50% CO2 concentration growth | |||||
| Source | Altitude | λ0 | f | ΔTS,100 | ΔTS,∞ |
| AR5 (2013) upper bound | 300 mb | 0.310 K W–1 m2 | +2.40 W m–2 K–1 | 1.3 K | 2.6 K |
| AR4 (2007) central estimate | 300 mb | 0.310 K W–1 m2 | +2.05 W m–2 K–1 | 0.9 K | 1.8 K |
| AR5 implicit central estimate | 300 mb | 0.310 K W–1 m2 | +1.50 W m–2 K–1 | 0.6 K | 1.3 K |
| AR5 lower bound | 300 mb | 0.310 K W–1 m2 | +0.75 W m–2 K–1 | 0.4 K | 0.9 K |
| M of B (2015) upper bound | 300 mb | 0.310 K W–1 m2 | +0.32 W m–2 K–1 | 0.4 K | 0.7 K |
| AR5 central estimate | 1013 mb | 0.215 K W–1 m2 | +1.50 W m–2 K–1 | 0.3 K | 0.7 K |
| M of B central estimate | 300 mb | 0.310 K W–1 m2 | –0.64 W m–2 K–1 | 0.3 K | 0.6 K |
| M of B upper bound | 1013 mb | 0.215 K W–1 m2 | +0.32 W m–2 K–1 | 0.3 K | 0.5 K |
| M of B lower bound | 300 mb | 0.310 K W–1 m2 | –1.60 W m–2 K–1 | 0.2 K | 0.4 K |
| M of B central estimate | 1013 mb | 0.215 K W–1 m2 | –0.64 W m–2 K–1 | 0.2 K | 0.4 K |
| Lindzen & Choi (2011) | 300 mb | 0.310 K W–1 m2 | –1.80 W m–2 K–1 | 0.2 K | 0.4 K |
| Spencer & Braswell (2011) | 300 mb | 0.310 K W–1 m2 | –1.80 W m–2 K–1 | 0.2 K | 0.4 K |
| M of B lower bound | 1013 mb | 0.215 K W–1 m2 | –1.60 W m–2 K–1 | 0.2 K | 0.3 K |
Table 2. 100-year (ΔTS,100) and equilibrium (ΔTS,∞) climate sensitivities to a 50% increase in CO2 concentration, applying Eq. (1) at the characteristic-emission altitude (300 mb) and, boldfaced, at the surface (1013 mb).
Once allowance has been made not only for the IPCC’s reduction of the feedback sum f from 2.05 to 1.5 W m–2 K–1 and the application of Eq. (1) to the relationship between TS and FS but also for the probability that f is not strongly positive, for the possibility that a 50% increase in CO2 concentration is all that can occur before fossil-fuel exhaustion, for the IPCC’s estimate that only half of equilibrium sensitivity will occur within the century after the CO2 increase, and for the fact that the CO2 increase will not be complete until the end of this century, it is difficult, and arguably impossible, to maintain that Man can cause a dangerous warming of the planet by 2100.
Indeed, even one ignores all of the considerations in the above paragraph except the first, the IPCC’s implicit central estimate of global warming this century would amount to only 1.1 K, just within the arbitrary 2-K-since-1750 limit, and any remaining warming would come through so slowly as to be harmless. It is no longer legitimate – if ever it was – to maintain that there is any need to fear runaway warming.
Quid vobis videtur?
Lord Monckton wrote: “Two conclusions are possible. Either one ought not to use Eq. (1) at the surface, reserving it for the characteristic emission altitude, in which event the value for surface flux density FS may well be incorrect and no one has any idea of what the Earth’s energy budget is …”
One applies equation 1 to the temperature at the characteristic emission altitude, not the surface temperature. When applying equation 1, you are assuming that the earth behaves like a blackbody, so you need to use its blackbody equivalent temperature 255 degK, not its surface temperature. In doing so, we lump all of the non-blackbody behavior into “feedbacks”. Lapse-rate feedback controls whether warming at the surface will be greater or less than warming at the critical emission altitude. When we talk about the no-feedback climate sensitivity of 1 degK for a 3.7 W/m2 forcing from 2XCO2 (without your factor of 7/6), we then make the assumption that warming at both locations is the same. Studies with climate models give a no-feedbacks climate sensitivity of 1.15 degK, because the earth doesn’t have a uniform temperature and the average of T^4 is greater than (average T)^4.
When you do calculations that treat the earth as a blackbody, the most you SHOULD say is that after an instantaneous doubling of CO2, the planet will warm SOMEWHERE until the 3.7 W/m2 imbalance is eliminated. Nothing in a blackbody analysis says that all of the warming couldn’t occur only in the upper atmosphere or just in polar regions. The surface emits only about 10% of the photons that escape to space, so it certainly isn’t required to warm. However, if you ASSUME equal warming everywhere, the no-feedbacks climate sensitivity would be 1.0 degK at the surface. However, by eliminating the possibility lapse rate feedback, a disguised REQUIREMENT for equal warming everywhere has been imposed. This requirement doesn’t directly follow from the physics of blackbody radiation – it’s a function of what we chose to call a feedback.
+1
The TOA is cold, and warming there does not dictate warming where we live. Warmista’s talk about adding energy to “the system” but they do not mention that it is the system’s five-miles-up area. I like your SOMEWHERE.
Michael: I’d like the “somewhere” that warming occurs to be mostly 5 miles above the surface, but I can’t convince myself that it will be. The drop off in temperature with altitude – the lapse rate – is controlled by the rate heat is convected upwards. A high lapse rate (rapid temperature drop with altitude) promotes more convection, but the convected heat increases the temperature of the upper atmosphere, reducing convection. So it is unlikely that all warming can occur high in the atmosphere, because that would reduce convection and leave the surface warmer. No simple calculation yields the average observed lapse rate, so we can’t predict from simple physics how the lapse rate will change.
Fortunately, increasing absolute humidity – a feedback – is certain to decrease lapse rate, so the GHE from increase water vapor is expected to be partially offset at the surface by a falling lapse rate. In other words, there will be more warming higher in the atmosphere than lower.
Saying that warming must occur SOMEWHERE shouldn’t be taken to imply it won’t happen at the surface of the earth. It is meant to remind us that calculation of a no-feedbacks climate sensitivity at the SURFACE from blackbody considerations requires ASSUMING that warming will be equal everywhere.
Gino, the atmosphere is not well mixed in absolute terms of water vapor and CO2 content, the main gases which absorb and emit IR. Lower atmosphere contains a larger absolute amount of these gases than the upper atmosphere. THEN…the temperatures are vastly different, and the IR emission is a strong function of temperature (but the IR absorption much less so).
Also, water vapor is not well mixed at all. It’s concentrated at lower latitudes.
Dr. Spencer,
Water vapor is widely variable in the atmosphere and rapidly reduces with pressure, but CO2 is quite well mixed: +/- 2 % of full scale from the North Pole to the South Pole, everywhere over the oceans and above a few hundred meters over land up to over 30 km height, except for a lag from NH to SH and near ground level to high altitudes, as human emissions are mainly in the NH at ground level. See:
http://www.nature.com/nature/journal/v288/n5789/abs/288347a0.html
A difference of 7 ppmv between tropopause and 33 km height on a level of 400 ppmv…
The highest variability is in the first few hundred meters over land where there are lots of near ground sources and sinks at work. But even if the first 1,000 meter was at 1,000 ppmv, that has hardly a measurable influence on the radiation balance (per Modtran)…
yes, which is what I was alluding to.
‘Sins of emission’ is very good.
It’s great that we can do all these diagrams and math to represent the earths energy budget. They are definitely useful in understanding the overall climate system/radiation balance. Probably most of the guesstimates are very close, many are right on the money. However, the amount of certainty in some and the final estimate, represented as the climate sensitivity for instance, is greatly exaggerated vs the reality of uncertainty.
Wouldn’t it be great if we did have all the correct equations to accurately represent all processes and only had to plug in all the accurately measured values to come out with the precise solutions to tell us what we need to know………out to the year 2100.
I lost some of my math skills from 35 years ago, when learning atmospheric science. However, I gained much more in observing the global atmosphere since then. What is clear, is the false illusion by some(more educated and better at math than me), that representing the atmosphere with mathematical equations has provided them with the power to project beyond what is realistic……..because you can’t have absolute certainty, when several elements that contribute towards your product have(not clearly defined) uncertainty.
I am with you here Mike. I got excellent grades in several semesters of engineering calculus, but have little ability to remember much of it now.
My take is a little different on why these equations seem unlikely, to me anyway, settle much of anything…at least not at the present state of understanding.
At every single place I have ever witness discussions of radiation physic and the math involved in all of these calculations, I have never seen a single one which did not have various individuals or factions of individuals from various disciplines and many of them apparently highly knowledgeable on both side, arguing vociferously and with great acrimony about disagreements over details large and small of nearly every single aspect of every part of the process.
I find it unlikely, under these circumstances, that there is even one single person who has everything figured out correctly.
Maybe there is, but I have yet to see evidence of such a shining beacon of calculative and physical genius in our midst.
Murray Salby sure seems convincing, but so do many others.
“Like”
Christopher
I can’t answer your question. However, I’d like to mention something which I believe has a bearing on it. Using average TSI throws off the scientists’ inputs for the radiative imbalance. It relates to your equation (4).
Let me begin by stating something that I’m sure you and many others know: using the assumed average TSI value of 1366Wm^-2 is a short cut which is supposed to average out the NH and SH summer variations in TSI of 1323Wm^-2 and 1413Wm^-2 respectively. This difference is due to the elliptical nature of the Earth’s orbit. Everyone accepts this averaging as being a reasonable expedient thus saving the labour of doing 365 daily calculations of equation 4 with different TSI inputs.
However, by conflating the average TSI figure with an equation that is derived from the T^4 element in the SB laws, it ignores the greater emissivity of the Earth’s surface during the SH summer months due to experiencing a higher equilibrium temperature. This won’t be offset by the lower emissivity of the NH summer months because the equilibrium temperature at both points in the Earth’s orbit is calculated using a T^4 input. Therefore, the surplus emissivity in the SH summer (over and above the average using the average TSI value in equation (4)) more than cancels out the deficit in emissivity during the NH summer. This in turn means that there is a seepage of heat flux during the SH summer that isn’t being accounted for in equation (4). Indeed, it is also the case for that entire half of the orbital ellipse which contains the SH summer though it’s much less marked towards the equinoxes.
The daily TSI readings are adjusted to 1AU so that at the height of the SH summer the higher figure of around 1413Wm-2 (depending on what the sun is doing that day) is scaled down to 1366Wm^-2 using the 1/r^2 orbital radius ratio and any daily fluctuations of a few tenths of a Watt are carried through and mirrored in the final daily figure. That then gets averaged with the other daily values to 1366Wm-2. If I recall, the measurements are actually 6-hourly. This means that the raw data is not being used in equation (4) and consequently, the surface emissivity when averaged over the year is too low due to the exponentially higher SH summer emissivity not accounted for due to the T^4 element. The result is that the calculated average surface temperature is too high and should be commensurately less.
There is a confounding issue here, which is that the Earth travels faster round the sun during the SH summer and so it experiences the higher TSI values for a shorter time. However, orbital speed is dependent on root 1/r, giving rise to a circa 3.3% variation in orbital speed over the year. TSI varies by circa 6.4% due to the 1/r^2 element. Seeing as the total energy received by the Earth’s disc is the integration of TSI over time and time is directly proportional to speed, it can be seen that the 3.3% speed-up during the SH summer isn’t enough to offset the 6.4% increase in TSI at that time. So, although the speeding up of the Earth dampens the extent of the surplus emmissivity that’s unaccounted for, it by no means cancels it out.
scute says…”However, by conflating the average TSI figure with an equation that is derived from the T^4 element in the SB laws, it ignores the greater emissivity of the Earth’s surface during the SH summer months due to experiencing a higher equilibrium temperature”
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This is not in fact evident as far as I know. The atmosphere cools in the SH summer, despite this greatly increased input. And yes, the albedo increases in the NH. But the solar input into the worlds oceans massively increases, and that energy is lost to the atmosphere for a time as well, but unlike the NH albedo lost, it is still within the earth. In my view there is much to be learned from the annual energy pulse.
Even if, for the sake of the argument, one allows the IPCC warming forecast of 4degC by 2100 due to manmade CO2, then thanks to Count Rutherford (Benjamin Thompson) and his famous experiment to help clarify the identity between Energy = Work = Quantity of Heat (all measured in joule, J) it is evident that in comparison to solar power reaching the Earth, the CO2 effect is about as trivial as a flea on the equator jumping off in an easterly direction will have in retarding the Earth’s rotation according to Newton, when compared to solar and lunar gravity effects. Unless, of course, anyone can show me where I may have gone wrong at http://tinyurl.com/ot2hlp4
Matt asks:
“Should it be “I ask only because I want to know” and not “I only ask
because I want to know.”
Yes: it should be “I ask only because I want to know.”
Whoever penned the other, like 99% of those writing today, has
no idea where to put the word ‘only’: like most submissions to WUWT.
They will say something like “The earth will only heat up when such
and such conditions obtain”, when what they really mean to say is
“The earth will heat up only when such and such conditions obtain.”
& etc ad nauseam.
Monckton. I just watched, on U-tube, you ask Salby a question on quantifying convective (evaporative) cooling at his March presentation. Here is an answer from Trenberth see below Fig 2 at
http://climatesense-norpag.blogspot.com/2014/07/climate-forecasting-methods-and-cooling.html
http://3.bp.blogspot.com/-ZBGetxdt0Xw/U8QyoqRJsWI/AAAAAAAAASM/ewt1U0mXdfA/s1600/TrenPPT.png
To quibble over mathematics, one first has to accept the central premise of the diagrams, which is that the majority of the atmospheric surface temperature comes from heating of the surface itself. I reject this premise, so all the mathematics that follows is meaningless. It should be pointed out that the mathematics have been calculated on the assumption that the central premise is correct and variables adjusted until the outcome matches observation. But there is no experimental evidence that can verify this premise to begin with. In short the diagrams are nothing more than illogical assumptions with no basis in reality. There is no Greenhouse Effect.
It is the mass of the atmosphere itself that causes temperatures higher than a planetary body with no atmosphere at equal distance from the sun. A conclusion that should be self evident when one observes temperatures on other planetary bodies with gaseous atmospheres in our solar system.
Still, if you persist with the paradigm then a simple graph with CO2 levels on the x axis and global mean temperatures on the y axis, plotted once in 1850 and once today, should give you three different types of mathematical trajectories to connect the two dots. All three of which, if you extend the line along each trajectory in both directions, will disprove some aspect of the Global Warming hypothesis. Try it for yourself and then reread both the claimed CO2 contribution for the greenhouse effect as a whole and the future temperature predictions for the 560ppm mark.
wickedwenchfan, you (and some others) continue to show your lack of understanding of the difference between lapse rate (due to gravity, specific heat of gas in atmosphere, and possible phase change of vapor to liquid/solid), which produces a temperature GRADIENT, and the cause of the actual temperature levels in that gradient. The actual temperature level is set by the energy balance at some average effective altitude of radiation to space. The change in effective altitude of radiation to space due to the change in quantity of optically absorbing gases (or particles) is the basis for the change in the atmospheric greenhouse effect.
I’ll tell you why answering your question (or trying to answer it) would give me a headache. Count the assumptions and approximations that go into each and every line of the algebra. Here is a partial list:
. Increase 
(which again is ot constant in space, time or wavelength) by just a tiny amount and because TOA insolation is LARGE, you drop it by a rather lot.
and an assumed homogeneous radiating surface are of 
and an assumed uniform constant average TOA insolation and an assumed unit emissivity and an assumed constant albedo when the real albedo looks more like these graphs:
* Unit emissivity — emissivity of the Earth’s surface is a) not a constant either in space or in time; b) varies with wavelength (one really has to do an integral to compute emissions/absorptions even from t very simple systems) b) does not have an average value of 1 (averaged over space, time, and wavelength).
* Assuming some “average” value for top of atmosphere insolation. TOA insolation varies by 91 watts per square meter over the course of the year, peak to peak, as the Earth orbits with its current eccentricity. It spends longer out where it is farther away, so TOA insolation isn’t a nice, symmetric sine function with a mean in the middle of the peaks.
* Surface homogeneity of other parameters like albedo (which, like emissivity, is not constant in space, time or wavelength). Again, this almost certainly matters, as it is necessary to assume a peculiar inversion in order to explain why the Earth is coldest at perihelion (southern hemisphere summer) and warmest at aphelion (northern hemisphere summer). In southern hemisphere summer TOA insolation is well over 1400 W/m^2 — a “forcing” of roughly 45 W/m^2 compared to your assumed mean, with NH summer forcing down in the ballpark of 1325 W/m^2 (being very generous with the subtraction). Note that albedo comes off of the top in a single layer model — if you want to look for a parameter that has a direct, immediate effect on the climate, albedo has to be close to number 1 as the total radiation that one has to balance is the TOA insolation times
* Then there is the dazzling detail in these figures. They have energy going up, going down, and the numbers are always for the entire planet. Have we a plausible way of measuring latent heat transfer as a function of height, integrated over the entire planetary surface, over a long enough period of time, over a spanning set of the other hidden variables in the system (things like the decadal oscillations, where to average over them would properly take centuries of detailed observations in depth) to be able to pin it down to within a percent? Two percent? Ten percent? And what are the assumptions that permit one to make ANY choice between these (Bayes theorem requires us to weaken any conclusions we draw according to the certainty of these assumptions).
One cannot plausibly solve the Navier-Stokes equations for the Earth at a resolution of 100x100x1 km^3 and expect to get a good answer for the climate decades into the future. One cannot solve the NS equations better by turning the entire planet into a single cell with an assumed cross-section to the sun of
http://www.climateforcing.info/Forcing/Forcing/albedo.html
Even if you google it up, you see estimates that range from 0.31 to 0.39. Let’s see:
P_1 = 1366(1 – 0.31) = 942.5 W/m^2 (TOA)
P_2 = 1366(1 – 0.39) = 833.3 W/m^2 (TOA)
P_1 – P_2 = 109.3 W/m^2
This gives one a small idea of the silliness of the entire enterprise. A change of 0.01 in albedo — roughly 3% — is equivalent to a change of roughly 14 W/m^2 in “average” TOA insolation. CO_2, in contrast, is estimated to be on the order of 1-2 W/m^2. Albedo changes are local, not global, and would have an amplified effect in the tropics.
Some very good questions are then — how accurately can we measure “global average albedo”? How variable is it? Does it have long term variability on top of short term variability? Is it part of a general nonlinear feedback process? Does it vary, nonlinearly, the same way in response to changes in the climate system at different points in space and time? And the big one:
Can we predict the albedo one, ten, a hundred, a thousand months into the future? Can we even predict the variation in the average albedo, whatever that means?
If we don’t know the albedo within 1%, and if we cannot predict the future evolution of the albedo within 3%, then using any single value of it in a computation that also assumes a constant TOA insolation and a planet with unit emissivity etc is not going to make much sense, is it?
If your only purpose is to show that there is sufficient uncertainty in climate science that the total climate log sensitivity to CO_2 could be anywhere from barely positive to 2-3 C — mission accomplished. But I don’t think your question has an answer outside of that.
rgb
Rgb, why do you think it has to be positive? How much is your “barely positive”?
Thanks, rgb.
I’ve been really struggling with Lord Monckton’s equations (never really mastered maths, keep going back to remind myself of the terms, etc) and trying to understand the consequences, and suddenly you put it into a proper perspective. A few earlier commenters – such as Joe Born and ‘Frank’, certainly have relevant things to say but I’m really relieved you came in! Proof or disproof of the CAGW by circuitous appeal to S-B is actually getting pretty tedious, and I don’t think we are going to learn anything that route.
Please keep those posts coming – saves my brain hurting too much
“does not have an average value of 1”
Trenberth says:
“The surface emissivity is not unity except perhaps in snow and ice regions, and it tends to be lowest in sand and desert regions, thereby slightly offsetting effects of the high temperatures on longwave (LW) upwelling radiation. It also varies with spectral band (see Chédin et al. 2004 for discussion). Wilber et al. (1999) estimate the broadband water emissivity as 0.9907 and compute emissions for their best estimated surface emissivity versus unity. Differences are up to 6 W m-2 in deserts, and can exceed 1.5 W m-2 in barren areas and shrublands. “
“TOA insolation varies by 91 watts per square meter over the course of the year, peak to peak”
They are calculating a “global annual mean energy budget”. They calculate the annual total. It adds up.
“Have we a plausible way of measuring latent heat transfer…”
Yes, and a very simple one. What goes up must come down. Total rainfall is quite well known.
“One cannot solve the NS equations better by turning the entire planet into a single cell “
They are not solving the Navier-Stokes equations.
‘how accurately can we measure “global average albedo”’
Global albedo is primarily measured using CERES and ERBE. This caused them to correct their 1997 figure from .313 to .298.
Nick Stokes continues to defend the indefensible. Let’s talk albedo: rocks, sand, dirt, vegetation in all its wondrous and beautiful variety, pavement, roofs, fresh water, salt water, ice, snow, waves, clouds, each with dozens to thousands of varieties. The satellites give us a value, which was wrong originally and is still wrong. The albedo of the Earth varies minute by minute and acre by acre. Sure, tell me you know what it is…
RGB: IMO, You exaggerate the difficulties. dF/F = 4*(dT/T) allows one to calculate small changes in F and T without worrying about emissivity. A 1% error in albedo and therefore F is a 1.5% error in dT. The error caused by assuming a uniform temperature is real, but modest (15%). The elliptical orbit is worth 91 W/m2 in terms of irradiance, but only 23 W/m2 in terms of the whole surface of the earth and 16 W/m2 post albedo. So post albedo radiation is about 240 +/- 8 W/m2 during the year. Using an annual average introduces negligible error. Temperature dependent changes in albedo are cloud and ice-albedo feedbacks and not relevant to no-feedback climate sensitivity. N-S is only needed if you want to know where warming will occur, not average warming without feedbacks.
Most of the error in calculating a no feedbacks CS of 1.0 degK comes from non uniform temperature being raised to the fourth power. A reasonable estimate of uncertainty might be +25% to -10%. All climate models agree with 1.15 degK within +/-1%, though that doesn’t include systematic errors. The biggest problem with treating the earth like a blackbody and calculating a no feedbacks climate sensitivity does not come from uncertainty – it comes from a lack of understanding of the assumptions being made in the calculation process. For example, Lord Monckton doesn’t understand why T should be 255 K instead of 288 K.
hi bob. while it’s been almost a year since i had time to work on a little project on the subject but a good example of what is going on with our system is that presently, the SH gets an average of around 3-5 W/m^2 more power in a year than the NH yet the NH is almost a degree C warmer on average. (this is mostly from sat. database info). It should be obvious that all those essentially unknowable little details you mentioned give substantially different values that are in the order of this CAGW effect that is being attempted to be measured. If one simply assumed to use the NH vs SH values from this, the conclusion would be that an increase in 4 W/m^2 would cause a decrease in T of nearly 1 deg C. LOL.
One thing I cringe at is the attempt at using the feedback eqn. It might be somewhat useful but I think the system is way too messy to yield anything useful. Breaking it down as a direct delta T effect by co2 and then seeing what delta F can occur additionally due to that delta T can be instructive. Absolute humidity increase is about the only thing one can get that is positive feedback capable of causing a radical increase in T. It’s easily shown co2 by itself can increase T less than 1 deg C for a doubling. With a relative humidity that is constant, the absolute humidity increase is far from a doubling for this (not even for a 5 deg C increase) and that means the CAGW crowd’s major helper isn’t going to be nearly enough. Basically, their case actually hangs on the notion that an increase in water vapor and evaporation will somehow result in less cloud formation and lower albedo.
Very interesting point.
But,,,,,as far as I can tell, in principle, it does not really matter what formula equation or method used for the calculation or a mathematical estimation of what is called climate sensitivity, for as long as the “scientific” definition of it is plainly wrong, and actually does not even play right and in accordance with any equation or method of such a calculation, any number assigned to the CS is wrong, in principle.
According to the CS definition, either while CS~3C as per IPCC or CS~0.7K as per L. Monkton there is an unavoidable accumulation of heat in the system.
So in both cases, which actually represent two different systems there will be an ever increasing of energy in the system……if for example in the CS~ 3C there will be ~1.6C continuing accumulation of heat for every CO2 “doubling” whenever that happens, in the case of L. Monckton .that will be ~0.4C….and even in the Monckton case the heat accumulation has the same problem of the ~ the same magnitude as in the IPCC for the “energy balance” book of such systems as the one in question.
An ~0.4C heat accumulation anomaly for a system with a CS~7K is as problematic as an ~1.6C anomaly for a system with a CS~3C….or an ~0.8C anomaly for a system with a CS ~1.5C…
So in principle either they all wrong or they all right, regardless of the actual CS number.
Or put it another way….. in principle either all AGWs are wrong or they all are right regardless of what CS scenario, either when catastrophic benign or mild all AGW scenarios must all be right or all be wrong, in principle….in accordance with the one principle hammered in to the CS definition, in a very AGW manner.
I don’t know how that may help Lord Monckton with his question…but at least he may consider the above when considering for which one of the AGW scenarios he goes and favors.
I have a hard time in considering how some one, who ever that one be, can have the courage to approach and try to understand or explain the intricacy of the Earth’s energy budget (in climatic terms) through the CS angle when the very definition of the CS violates the very principles and essentials of the methods the formulas or the equations used to calculate it….but maybe that is just me, probably missing some thing here! (hopefully not my mind 🙂 )
Lord Monckton, no disrespect meant, honestly, and I still do like very much your CS estimate…:-)
Apart from all this, I do really appreciate and value your courage shown through years now, in this particular issue.
Cheers
Ah, so you’ve finally accepted what I said when discussing your ‘scibull’ paper, that the Planck feedback is a feedback and should be treated like one. Since it is THE feedback that keeps the planet stable it must be viewed that way.
You have come up with a simple but effective article. The only defect I can see is that it relies heavily on gross assumption, ballpark figures about albedo. For example I doubt that saying spectral emissivity is 1 across the spectrum is realistic.
How would a somewhat lower figure affect the results?
Also, since I’m sure you’d want to get the terminology correct you should correct the following:
“where F is radiative flux density in W m–2”
That is the total flux leaving the body, not the flux density. There is no surface area, shape or dimension implicit in that formula.
Good article.
No, the Planck “feedback” is not treated in the climate-sensitivity equation in the same way as the true feedbacks.
“No, the Planck “feedback” is not treated in the climate-sensitivity equation in the same way as the true feedbacks.”
There are two ways to do it, either treating all the responses the same (in which case they are all called feedbacks, as in IPCC AR5) or by splitting out the Planck (Stefan-Boltzmann) response and calling the rest feedbacks. Some authors use one, and some the other. Mathematically identical, but semantically confusing.
Doing it the first way, the total feedback must be (and is) net negative for a stable system. Doing it the second way, the total feedback must be less than unity for a stable system. In that case positive or negative feedback means a temperature change greater than or less than the Planck response.
In the climate sensitivity equation, the initial forcing and separately the sum of the true feedbacks are multiplied by the Planck parameter, by that parameter alone, and not by ant of the true feedbacks. For a discussion, see Roe (2009).
While the math may be interesting what is often left off is the assumptions. The primary assumption is the well mixed assumption. The primary gases are probably well mixed (nitrogen and oxygen). The others my guess are not well mixed at all. This raises considerable doubt to the use of the log function on some of the “green house” gases when indeed we do not know their actual concentrations in each instance.
Whiten You say
“as far as I can tell, in principle, it does not really matter what formula equation or method used for the calculation or a mathematical estimation of what is called climate sensitivity, for as long as the “scientific” definition of it is plainly wrong, and actually does not even play right and in accordance with any equation or method of such a calculation, any number assigned to the CS is wrong, in principle.”
I agree – but surprisingly so does the IPCC which has itself now given up on estimating CS – the AR5 SPM says ( hidden away in a footnote)
“No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies”
but paradoxically they still claim that we can dial up a desired temperature by controlling CO2 levels .This is cognitive dissonance so extreme as to be crazy.
For a complete discussion of the inutility of the GCMs in forecasting anything or estimating ECS see Section 1 at
http://climatesense-norpag.blogspot.com/2014/07/climate-forecasting-methods-and-cooling.html
The same post also provides estimates of the timing and amplitude of the coming cooling based on the 60 and especially the millennial quasi- periodicity so obvious in the temperature data and using the neutron count and 10 Be data as the most useful proxy for solar “activity”.
Thank you Dr. Page, RGB at Duke, Whiten (and many others above) for these comments.
I too very much appreciate and support the courage and efforts of Lord Monckton, but the points you all bring up contain many ideas which float around in my head in some form, but I am usually not concise or eloquent enough to verbalize the ideas and jot them down in a way which is coherent.
Reading this article and the comments make me feel much better about what I think I know, and what I am sure that no one really “knows”.
Everything I read from the point of view of CAGW, or from those who believe those who preach it, makes me feel very bad (At turns angry, dismayed incredulous, fatalistic, mirthful, and sometimes physically ill), every time, and these feelings seems to be getting worse.
Where is it going to end? So many are actually doubling down on the lunacy, and so many of these have great influence and power.
RE:WARMING IN THE PIPE
If you do the math, you’ll find that it would take over 500 years at the current “energy imbalance” to raise the temperature of the oceans just 1C. And even with that, the difference between the ocean temperature and the average surface temperature would still be about 15C (making little difference in heat absorbed). Because of this, with respect to anthropogenic emissions…the ocean is effectively a bottomless pit of thermal storage.
Only if you assume we have to heat the whole volume of the ocean before atmospheric effects become significant
In the words of Darth Vader “Nothing can stop that now”. The heat exchange between the warm surface and the rest of the ocean is far more effective than between surface and air. To claim otherwise is to claim that 2nd Law is violated (see here).
Even if hot surface water temperatures did raise atmospheric temperatures, it would be temporary. As the surface energy spreads throughout the ocean, temperatures would drop. There is no getting around the fact that a steady state increase is extremely difficult to pull off without many orders of magnitude more energy.
VikingExplorer
June 28, 2015 at 10:06 am
Unless I do misunderstand your point above, the only violation of the 2nd law you mention is in the interpretation of the given event, like in your case.
There is actually no violation of that 2nd law, unless that will satisfy and please one’s beliefs and predetermined world view.
When the energy (heat) moves from the oceans to the atmosphere, both the surface and the atmosphere are expected to have a warming-up signature, and in the mean time the CO2 emissions go up.
A significant discrepancy in this one, like one in question lately, when and where the warming signature of the surface is considerably higher than that of the atmosphere, does not necessary mean any violation of that 2nd law, because simply by relying on that very 2nd law you may just have the answer to it.
If the atmosphere is losing energy (heat) to the outer space than in this particular case the surface will be showing warming for a while when in the same time the atmosphere may show no any warming at all.
That actually explains why in the first place the CO2 emissions keep going up with no any atmospheric observed warming and why actually the heat is and must be moving from the oceans into the atmosphere (and out to the deep freezing space).
One’s beliefs and world view can not actually violate or break such a law.
cheers
“If there is an imbalance, a change in mean temperature will restore equilibrium.” There is no equilibrium. Earth is a system that’s not at equilibrium (a rotating body with a Sun close by and the cold space around cannot be). A dynamical, complex, non linear system that evolves at non equilibrium. There is not even a dynamical equilibrium. And mean temperature has nothing to do with an equilibrium, anyway. It’s an unphysical quantity. For a system that evolves towards equilibrium, there are other mechanisms that drive it, the mean temperature is not among them.
Exactly. poitsplace and Somebody are exactly correct.
No comment on the overall point, but the above is incorrect or misleading. The statement is incorrect because it’s missing two things. (1) Any hint that this is a transient phenomena of unspecified time scale. (2) Any reference to the size of the reservoir.
An unbalance simply implies that the energy level of earth would change, and that would be reflected in some internal temperature or phase change or work performed. Mercury is still warming up, and Jupiter is still cooling down.
Consider Lake Erie, where the water level is determined by water coming in (Lake Huron, rain, rivers) minus water going out (Niagara Falls, evaporation). Most of these processes are not directly dependent on the water level.
The inflow from Huron depends on the level of Huron minus the height of the land blocking the flow. The outflow depends on the level of Lake Erie minus the height of the land blocking the flow. An increase in water also increases surface area, increasing evaporation.
Lake Erie may be slowly evolving from a lake to a river that flows from Lake Huron to Lake Ontario. However, there is no physical law of equilibrium that is striving to restore balance.
In this analogy, claiming that increasing CO2 would raise the temperature of Earth would be equivalent to claiming that blocking off a small part of the American Falls would raise the level of Lake Erie.
Even IF man were raising the radiative resistance slightly, there are several possible consequences:
a) The incoming radiative resistance is also raised (20 – 24% of TSI and a majority of near infrared radiation is absorbed by the troposphere).
b) The extra energy could cause additional phase change or work to be performed (additional emergent phenomena as Willis describes it).
c) It could simply result in a warmer troposphere. Any down-welling radiation from this warmer troposphere is simply reducing how much the troposphere is warmed. The TOA is thus warmer than it otherwise would be, and radiates more to space.
res mihi quidem uidetur esse incerta.
positum est certitudo quaedam
Certi sumus de incerto vis an non pro certo habere possumus et incerta comprehendis?
“Do you mean the uncertainty we are certain of, or do you include the uncertainties we can not be certain of yet?”
difficile est dictu quod incertum quoque uidetur utrum incerta re uera scimus an nescimus. et de eo quod nescimus nec certi neque incerti esse possumus.
Good work L V M of B.
I see you have been reading my email exchanges on S-B Law and role of emissivity since April 12, 2015. You are closing in on the vanishingly small effect of CO2 on global T. Thanks again for editing http://www.principia-scientific.org/professor-singer-finds-co2-has-little-affect-global-temperature-v2.html
The forcing of interest is not F but [CO2], which affects emissivity ε. We want
dT/dCO2 = dT/dε * dε/dCO2
Rearranging S-B Law for
T = (F/εσ)^0.25
dT/dε = 0.25(F/εσ)^-0.75 * – (F/σ) ε^-2 = -0.25(F/σ)^0.25 * ε^-1.25 0
Therefore,
dT/dCO2 < 0.
This means cooling, so long as assumption F independent of [CO2] is valid.
To estimate how much, all you have to do is integrate atmosphere ε(T, P, C) through altitude to find bulk atmosphere effective εa and dεa/d[CO2] and use laws of radiant energy transfer to quantify the change in atmosphere Fa and surface Fs = 239 – Fa to find global ε and corresponding T’s (T, Ta , Ts).
Better to think of S-B Law giving F or I, intensity, irradiance, rather than flux. It is only flux when surroundings are at T = 0k. Driving force for radiant energy transfer from 2 to 1 is I2 – I1.
Mr Latour, in the dishonest fashion of the Sloyers, suggests that I am “closing in” on their position. He also suggests I “edited” his nonsense dishonestly stating that Prifessor Singer is also “closing in” on the “there is no greenhouse effect” rubbish. Professor Singer accepts, as does everyone who accepts the results of oft-repeated experiments, that there is a greenhouse effect. Accordingly, my alleged “edit” was confined to removing references to Professor Singer’s name.
For some years, the corrupt organisation that promotes the nonsensical notion that there is no greenhouse effect has freudulently used the names of many eminent scientists to attract donations by falsely asserting that they support its bizarre belief system. That matter is now before the investigating authorities, who are reviewing the evidence and will decide in due course whether and whom to prosecute for obtaining a pecuniary advantage by deception.
It would be wiser, therefore, if Mr Latour were to stop using Dr Singer’s name and, for that matter, mine in any context that might in any way be interpreted as implying we do not think there is a greenhouse effect,
Mr Latour is additionally and characteristically dishonest in his false implication that I am shifting to a position I have not held from the outset. In my first ever public statement on the greenhouse effect I said our enhancement of it could be expected to cause some warming, but on balance not very much. That remains my position and, so far at any rate, the last nine years have indicated that I am correct.
There is no incompatibility between recognising that there is a greenhouse effect and expecting an enhancement of that effect under modern conditions to be small.
The authorities have also been asked to investigate whether the true purpose of the corrupt organisation that thus makes free with the names of eminent researchers who do not in fact endorse its lunatic notions exists precisely for the purpose of discrediting not only them but all skeptics by creating confusion through its repeated false suggestions that various prominent skeptics do not believe there is a greenhouse effect,
‘Quid vobis videtur?’
Cacoethes carpendi 😉
Good work L V M of B. I see you have been reading my email exchanges on S-B Law and role of emissivity since April 12, 2015. You are closing in on the vanishingly small effect of CO2 on global T. Thanks again for editing http://www.principia-scientific.org/professor-singer-finds-co2-has-little-affect-global-temperature-v2.html
The forcing of interest is not F but [CO2], which affects emissivity ε. We want
dT/dCO2 = dT/dε * dε/dCO2
Rearranging S-B Law for T = (F/εσ)^0.25
dT/dε = 0.25(F/εσ)^-0.75 * – (F/σ) ε^-2 = -0.25(F/σ)^0.25 * ε^-1.25 0
Therefore, dT/dCO2 < 0.
This means cooling, so long as assumption F independent of [CO2] is valid.
To estimate how much, all you have to do is integrate atmosphere ε(T, P, C) through altitude to find bulk atmosphere effective εa and dεa/d[CO2] and use laws of radiant energy transfer to quantify the change in atmosphere Fa and surface Fs = 239 – Fa to find global ε and corresponding T’s (T, Ta , Ts).
Better to think of S-B Law giving F or I, intensity, irradiance, rather than flux. It is only flux when surroundings are at T = 0K. Driving force for radiant energy transfer from 2 to 1 is I2 – I1.
Your article you included with your link has a logical error. In your article, you claim that a body that has a higher emissivity is cooler than a body with lower emissivity under the same constant radiant flux. One could envision the inside of a large sphere that is a perfect blackbody emitter (but not necessarily). We then place another, smaller sphere in its center. Independent of the emissivity of the inner body, it will reach the same temperature as the outer body. It reaches its equilibrium only faster, the higher its emissivity is! Otherwise, you could run a heat engine between these two bodies, and that violates the 2nd law of thermodynamics.
See my reply to Mr Latour’s drivel a little upthread.
“Professor Murry Salby has estimated that, after the exhaustion of all affordably recoverable fossil fuels at the end of the present century, an increase of no more than 50% on today’s CO2 concentration – from 0.4 to 0.6 mmol mol–1 – will have been achieved.”
A 50% increase in CO2 is unlikely as CO2 would partition into the oceans at 50 to 1. Because of this effect, if we burned everything we have, everything, our homes included, we might be able to raise atmospheric CO2 by 20% The oceans work against us as, for every CO2 added to the atmosphere, 50 are added to the ocean as it tries to go to equilibrium.
higley7,
You forget the time factor: until now, about halve the human emissions per year as mass are absorbed by the oceans and the biosphere. The whole carbon cycle seems to behave as a linear process in disequilibrium, where the sink rate is directly proportional to the extra quantity (=pressure) in the atmosphere above steady state for the current (ocean) temperature, which is around 290 ppmv.
The past (1960) and current (2012) sink rates show a similar e-fold decay rate of slightly over 50 years, or a half life time for the excess CO2 of ~40 years. That is not fast enough to remove all human CO2 in the same year as emitted. If the emissions go on as was the case until now, that is slightly quadratic over time, we can easily reach far higher levels (~800 ppmv for “business as usual”). Only if human emissions level off or drop, the levels in the atmosphere will level off too until emissions and net sink rate are equal, or drop to steady state if all emissions ceased.
Finally, the human emissions will be redistributed over atmosphere, biosphere and (deep) oceans, but that needs a lot of time, as the uptake speed of oceans and vegetation is limited.
Consider a REAL greenhouse in full sun. If the greenhouse has no ventilation, how long before the CO2 is effectively depleted?
Hint: it does not take days (“a lot of time”).
Geran,
Take the same greenhouse and add a lot of manure and/or plant debris: the CO2 levels will go up to 1,000 ppmv, only somewhat lower during the day for weeks to come…
The big greenhouse called earth has several carbon cycles, where the exchange between atmosphere and biosphere is about 60 GtC in and 61 GtC out over the seasons: an uptake of some 1 GtC extra into the biosphere caused by the 30% extra CO2 pressure in the atmosphere. See:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Thus removing the current 230 GtC extra CO2 in the atmosphere above the steady state equilibrium for the current temperature (per Henry’s law: ~290 ppmv) will take a lot of time…
“If the emissions go on as was the case until now, that is slightly quadratic over time, we can easily reach far higher levels (~800 ppmv for “business as usual”).
No we cannot. There is no credible scenario where we get to 800ppm this century.
Here’s why:
1. Carbon uptake has consistently increased and the ocean uptake will increase further, on a path that increases the greater the concentration of Co2. I’ts about 5 GT of carbon, over 50% of the 9GT of carbon emissions. As ppm of Co2 goes up, so does rate of carbon uptake; when we get to 550ppm, the carbon uptake will be 10 GT, equal to current emissions. So if all we do is simply keep emissions at current levels, we will never go above 550ppm. The ocean sink is so massive (unlimited actually, due to calcium carbonate sedimentation), we could emit 10 GT of carbon for 280 years, and the oceans would soak up 7/8ths of it.
2. It’s not credible to suppose emissions will increase quadratically in coming decades, in 2014 it did not increase AT ALL over 2013. If trends continue, my 8 year old son will be 50 feet tall by age 35. OECD countries have flatlined and now even reduced emissions, and the rise of emissions due to China has now ended. The US doubled GDP since 1970, yet uses less oil per capita. With or without carbon taxes or limitations, we will not emit that much more carbon, because we can grow without increasing energy use.
3. There’s not enough economic growth to sustain much higher emissions. Even a doubling of emissions globally would require 4x – 5x increases in developing nations’ emissions, but that implies more growth than is actually happening *AND* a reversal of the trends towards renewables and energy efficiency.
4. We are increasing Co2 by 2 ppm per year. Given #1, even if we increase emissions, the carbon sinks will grow as well, and given #2 and #3 its very unlikely that emissions will grow that much. A 2% increase/ year in emissions will lead to about 550 ppm by 2100.
5. Technology is moving forward at a pace that implies renewables will be cost competitive and displace fossil fuels by 2040.
6. Since the alarmists are hyping up this threat, enough to force commitments to emit WELL BELOW the 2% increase per year, its likely we will not even hit 550ppm.
“A 2% increase/ year in emissions will lead to about 550 ppm by 2100.”
I should correct/clarify myself. I meant 2% increase until 2040 not 2100. I did an analysis wherein we estimate carbon uptake as increasing as ppm rise, and the emissions are increase 2% per year until 2040 and then flatlines at around 16GT emissions almost double current emissions – that leads to 585 ppm. if you project a 1% decline in emissions after 2050, bringing emissions from 16GT to 10GT it goes to 550ppm.
The uptake assumption is that it increases linearly with increasing ppm.
In short, realistic scenarios in which we global energy use in 21st century track what has happened to OECD nations in the past 40 years would lead to 550-580 ppm by 2100.
Given both technology trends and uptake trends, we could make 600ppm the upper limits. And given the work that shows TCR is around 1.3-1.4C, the upper limit of temperature change now until 2090 is about 0.7C.
A 2% increase ad infinitum (which does lead to 40 GT of output per year and higher Co2 level), as I noted, is unrealistic on many levels (resource constraints, defies economic models, contradicts historical consumption patterns/trends).
Hey Pat, what are you feeding that kid?
You are going spend a fortune on clothes and shoes!
patmcguinness,
If and only IF the emissions don’t grow as “business as usual”, then you may be right, but until now the CO2 levels have grown with the worst scenario. One year of lower emissions isn’t a trend, the more that a lot of Western countries (and even China) didn’t grow in economical activity or less than expected.
As the response of the oceans and biosphere to the increased pressure in the atmosphere seems to be quite linear, steady emissions indeed would lead to a new steady state where emissions and sinks are equal but “business as usual” can lead to 800 ppmv and more in the atmosphere…
Thus everything depends of the future emissions…
Seawater dissolved inorganic carbon (DIC) is known to be about 2.2 millimolar at the surface. The air in contact with that surface is 0.4 millimolar CO2. So, 2.2/0.4 equals 5.5.
Basically, for 65 molecules of CO2 added to the atmosphere, about 55 will end up in the ocean and 10 will remain in the atmosphere.
That 50 to 1 number comes from using equal volume ratios.
For the change in CO2 from 280 to 400 ppm, the difference is 120 ppm. Basically, the same ratio applies, with about 100 ppm entering (and staying) in the ocean, and the remainder, about 20 ppm remaining in the atmosphere. This is consistent with many other approaches to the estimate of how much of the human CO2 is actaully in the atmosphere today, about 20 ppm.
CO2 never “accumulates” in the atmosphere, it is part of a flowing biogeochemical river with huge abiotic (ocean) and biotic exchanges.
Does any of this explain why CO2 in the atmosphere seems to be on a more or less linear trend, even while CO2 emissions have increased, and the rate of increase is also increasing?
Menicholas,
All three observations are slightly quadratic: human emissions, increase in the atmosphere and increase in net sink rate. There are of course year by year (10-90%) and decadal (40-60%) variations in sink rate, mainly caused by temperature, but the average sink rate is 45-50% of the emissions over the past 115 years, making that the increase in the atmosphere is 50-55% of the emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_emiss_increase.jpg
bw,
You forget a few points… Solubility of CO2 in fresh water is very low. In seawater about a factor 10 higher (the buffer/Revelle factor), but even so, including all buffering, a 100% change in the atmosphere results in a 100% change in free CO2 in seawater, per Henry’s law, but only a 10% change in DIC, as free CO2 is only 1% of all forms of carbon. The rest is 90% bicarbonate and 9% carbonate.
That means that the 30% CO2 increase in the atmosphere is good for a 3% increase of DIC in the ocean surface or from ~1000 GtC to ~1030 GtC. Far from your 50:1 ratio.
The 50:1 ratio may apply to the deep oceans, but the exchange rate of the atmosphere with the deep oceans is much more restricted to polar sinking and equatorial upwelling, each only 5% of the ocean surface.
Thus while the ultimate distribution may be 1:50, that needs a lot of time and as human emissions still are increasing year by year, that accumulates in the atmosphere, because the response of the sinks is not fast enough…
FE, what about dissolving of into fresh water as raindrops fall. Is it plausible that the pressure, friction, turbulence and mixing within a drop allow a significant amount of CO2 to be absorbed while a drop falls?
There’s another way of getting the ocean uptake amounts. The keys are to know the amount of DIC (dissolved inorganic carbon) and the revelle factor, which calculates how a change in atmospheric ppm changes the total DIC %age. basically, most of the DIC is in the form of carbonates, and adding CO2 changes the chemistry ratios of Co2, HCO3 and H2CO3 that make up the DIC. The amount of DIC in the whole ocean is MASSIVE – 37,000 gigatonnes of carbon as DIC. This is 70x the amount of Co2 in the atmosphere (at about 560 GT or so). the revelle factor is about 10.
What this means is that if atmospheric Co2 goes up by 30%, you divide by 10 and DIC in the ocean goes up by 3%. You multiple that by the ocean DIC. so what if we double CO2?
then ocean DIC can go up by about 10% of 37,000 GT, or 3700 GT. Since double CO2 means going from 560GT to twice that, the oceans will take up 3700GT vs the atmosphere 560GT.
Hence, over time (and this is a slow process, taking up about 1.6 GT of CO2 from surface ocean to deep ocean per year), 7/8ths of emissions will end up in the ocean. It also means that some level of emissions are such that we will not increase Co2 ppm, and that zero emissions will actually cause Co2 ppm to go down.
Mr. Engelbeen,
I appreciate the response, but I am not sure that you have explained anything.
BTW I dispute the temperature part of the graph you posted.
I do not think it represents objective reality.
Curious, has a rate of diffusion of dissolved gasses and ions into the water column ever been measured?
In other words, how long might it take for CO2/bicarbonate/carbonate in surface water to diffuse to the deep ocean?
Do we have a number for that? I understand it must be rather low, but not sure how low.
Aaron,
I once calculated the amounts of CO2 in rainwater: while that dissolves carbonate rocks (but even that needs millions of years to carve the beautiful caves…), what is dissolved at where the raindrops form is maximum 1.32 mg/l at 0°C. 1 l rainwater is formed out of 400 m3 of air and takes time to form, thus the water there is probably completely saturated with CO2. Even so, that hardly affects the CO2 levels at height. While the drops fall down, temperature in general increases which makes that even less CO2 is retained…
1 l/m2 gives 1 mm rain where the drops fall down. If all that water evaporates, setting all CO2 free, that gives less than 1 ppmv extra in the first meter of air without wind mixing…
Thus while the total water cycle is enormous and a lot of CO2 is moved along, that is hardly measurable in the concentrations, both in the high atmosphere and near ground.
Menicholas,
The temperature trend is from HadCRU ocean temperature. No matter which other trend you take, the trends are similar, but one can doubt the slope. What is sure is that the impact of temperature (variability and trend) on the CO2 levels is restricted: 4-5 ppmv/K for short term variations up to 8 ppmv/K for (very) long term influence.
That is also what Henry’s law says for the solubility of CO2 in seawater (4-17 ppmv/K in the literature).
In the above graph it is clear that the huge variability in temperature has little influence on the CO2 increase in the atmosphere. Neither has the trend, as the period 1945-1975 shows a cooling and 2000-current is flat while CO2 levels simply follow human emissions.
Diffusion of CO2 in water is very slow. Only by wind and waves the mixing between ocean surface layer (the “mixed layer”) and atmosphere is fast. Besides some carbon particles (organic and inorganic – shells) of dead plankton and fish excrements there are only limited exchanges between the ocean surface / atmosphere and the deep oceans.
There are several works which have followed human CO2 into the deep oceans, one of then is here:
http://www.pmel.noaa.gov/pubs/outstand/sabi2683/sabi2683.shtml
As there is a slight difference in 13C/12C ratio between fossil fuels carbon and oceanic carbon, the changes can be traced back.
Other general exchanges are know by using tracers like the 1950-1960 peak in 14C caused by the open air nuclear bomb tests and millions of measurements over the years by research ship cruises from the surface to depth…
Here is an example of the fatal flaw in the “energy budget” posited by the climate science community. And you can do this in your front yard (but not so easily in the winter).
Take two pieces of pipe, same diameter/length. One made of steel (or copper) and the other made of PVC (or another plastic material). Paint them both gray to make the albedo’s identical (not that it matters). Place them both on your front lawn exposed to bright summer sunlight. Wait a while.
Both pipes are receiving the same incoming energy flux (units of Watts per Surface Area), both will heat up to about the same temperature as the surrounding grass. Convective cooling will keep them both at about the same temperature.
Now pick one up in each hand, in “sunny” areas of the Earth you are likely to wince in pain and drop the steel pipe while the plastic pipe will feel comfortable to hold in your hand.
Why ? Thermal capacity and thermal diffusivity.
The metal pipe has absorbed more thermal energy and stored it internally than the plastic pipe. The metal pipe has more thermal capacity so it can hold, contain or “trap” more thermal energy than the plastic pipe.
The second part of the explanations has to do with thermal diffusivity, from a systems perspective thermal diffusivity is essentially a measure of the velocity of heat flowing through a material. The velocity of heat flow through metals is faster than the velocity of heat flow through human skin/flesh.
When you pick up the metal pipe the heat flows quickly from the interior of the pipe into your hand at the pipe/skin interface, this causes the pain you feel.
When you pick up the plastic pipe there is less thermal energy in the pipe and it travels more slowly from the interior of the pipe to your hand. Thus it feels comfortable to hold.
You cannot perform a correct energy budget analysis of the thermal energy “trapped” in a material after being absorbed from light radiation WITHOUT properly considering the thermal capacities of the materials involved in the system.
Yes, you can make a “budget” and put measured values into said “budget” but it is a complete “made up” version of what is happening. And it will not provide any useful or predictive information about what the temperatures will be at locations in the system.
The thermal capacity of the Ocean’s of the Earth is huge, the thermal capacity of the gases in the atmosphere is much smaller. The thermal capacity of the “GHG’s” in the atmosphere is miniscule in comparison. The GHG’s are simply “along for the ride” when it comes to controlling the”average” temperature of the Earth and have NO EFFECT (i.e. climate sensitivity = 0.00000000).
Cheers, KevinK
I love this, because it makes sense and yet nearly everyone in the “climate science” community seems to disagree.
I do not. I think until someone can explain exactly how or why this is not correct, it is an unaccounted for piece of information.
And there are a very many such unaccounted for pieces of information.
I would like to add to this comment the following perspective. IMHO there are three different groups of gasses that participate in thermal “storage” in our atmosphere. The first group are the transparent gasses that are in the greatest abundance, the second set are the “passive” GHG which have absorbance bands in the IR spectrum (of which CO2 has received the most attention), and then the final gas is by far the most significant – the “active” GHG H2O. In the atmosphere water is an even more significant an energy storage/energy transfer molecule than these simplistic “energy budget” illustrations account for or than your example of a metal pipe versus plastic pipe suggests. Why? because not only does water have a significantly higher heat capacity in all it’s phases, but it is the only molecule in any of these discussion that ACTIVELY changes phase to store energy, then MOVES vertically and horizontally in a phase changed state to transfer energy, then changes state again to ACTIVELY release the stored energy. IMHO, this process sucks up radiative energy near the surface then vertically transfers it to the upper atmosphere, then in two separate phase changes, transfers the radiative energy back to space effectively super cooling the planet right where cooling is needed and transferring heat to other regions that need heat. Again IMHO, the fact that there is SO MUCH water present in the equation, the earth’s atmosphere is effectively buffered to rarely ever exceed temperature extremes. In an ACTIVE system like earths atmosphere, a passive 2D attempt to model an energy budget that is based on mythical temperature, and incomming and outgoing radiation AVERAGES is a fool’s errand.
Don,
The radiative budget includes the energy absorbed in evaporation of water vapor and released in condensation of water vapor. It’s the 80 W/m^2 labeled “evapotranspiration”.
The value is known reasonably accurately since it is an easy exercise to derive the amount of energy transported given the heat of vaporization of water (which does depend on temperature at which the evaporation / vaporization occurs, but fairly weakly) and the average amount of precipitation.
DonV, yes, in my example I was referring to the “GHGs” other than water.
We are very lucky to have water in all it’s states on this planet, without it we would see the wild temperature extremes observed on the Moon. As a resident of Upstate NY I do hate to think about scraping the ice off my car windshield on a January morning if it was minus 180 F outside. Heck minus 10 F seems plenty uncomfortable enough for me.
Usually the Fool’s on an errand are the very last ones to recognize the folly of their actions.
Cheers, KevinK
joeldshore says..
June 27, 2015 at 4:17 pm
Don,
The radiative budget includes the energy absorbed in evaporation of water vapor and released in condensation of water vapor. It’s the 80 W/m^2 labeled “evapotranspiration”.
The value is known reasonably accurately since it is an easy exercise to derive the amount of energy transported given the heat of vaporization of water (which does depend on temperature at which the evaporation / vaporization occurs, but fairly weakly) and the average amount of precipitation.
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How much energy (on a watts per sq. meter basis) does it take to accelerate the hydrological cycle, and to grow 35 percent more bio-life? I only ask because I want to know.
Kevin,
Your argument is complete nonsense on a few levels.
(1) The GHG’s rapidly thermalize with the other molecules in the atmosphere, so the heat capacity of just them is irrelevant. It is the heat capacity of the entire atmosphere that is involved.
(2) Your whole picture is incorrect. The thermal energy is not trapped in the GHG’s or the atmosphere; it is trapped BY the GHG’s but mostly stored in the ocean. Your argument is akin to saying that one of those space blankets (https://en.wikipedia.org/wiki/Space_blanket) can’t possibly be useful because their mass…and hence thermal heat capacity…is much smaller than that of your body.
(3) All actual serious calculations of the climate system, especially dynamics (i.e., how long it takes for temperatures to change) are done using the relevant heat capacities. So, you are implying that climate scientists are ignoring something that they aren’t.
1) All of the energy must flow through the “GHGs” thus the “GHG” must have enough thermal capacity to store (even temporarily) all of the energy. You are incorrect.
2) The human body is a “source of heat” (or a heat supply) your body “burns” fuel and makes heat. This enables a “space blanket” to make you more comfortable. The surface of the Earth is a “reservoir of heat” it is not a source of heat. A “space blanket” on a rock in your front yard will not make the rock warmer.
3) The “climate science” “energy budget” cartoon (the original topic of this post) does not appear to have any dynamics involved in the calculations anywhere. Did I perhaps miss the units of time somewhere ?
Kevin,
1) So, can you show us your explicit calculation that there are not enough GHGs in the atmosphere to store the thermal energy for the very short time until the excited CO2 molecule thermalizes with the rest of the atmosphere? Since this claim contradicts a lot of known science, it would certainly be quite a discovery if this were true!
2) The sun is a “source of heat”. So, your arguments amounts to the claim that the greenhouse effect would not exist without the sun. I don’t think you are likely to get much argument on that point.
3) That’s my point…Since it does not involve dynamics, the heat capacities do not directly enter into it. However, once you start to try to calculate what happens over time if you change the energy balance, then the heat capacities are certainly important.
I think it will make the rock warmer if the rock is in the sun. Or, it will take longer rock to reach the ambient temperature when the ambient temperature changes.
But the earth is not a simple rock, and the atmosphere not a simple blanket.
Kevin, You make a fundamental mistake by confusing, on the one hand, the transient transfer of heat from one body to another (which as you correctly say, depends on the source material’s thermal capacity and surface diffusivity), and, on the other hand, the long term steady state transfer of energy from one body to another. There may be other flaws in the energy budgets under discussion here but they are certainly not due to the effect you describe.
If there are indeed real flaws in long term steady state energy flow budgets, it interesting how nobody ever suggests better numbers. Instead people tend to criticise them on various spurious ‘transient effect’ grounds. The figures in the Kiehl-Trenberth diagram do balance and should not be dismissed just because Trenberth himself happens to be a CAGW alarmist. Likewise, Monckton’s calculations relate to long term steady state averages and so should not be criticised using arguments about irrelevant short term ‘transient’ effects.
We skeptics do ourselves a profound disservice if we fight the wrong targets.
Great effort. Keep digging. Soon you may find that CO2 does NOT “produce warming”.
Where did anyone say CO2 does not “produce” warming? I’ve also never heard anyone deny that flushing a toilet raises sea level either for that matter.
One problem is that the energy cartoon budget is 2 dimensional whereas we live in a 3 dimensional world, and insufficient thought has been given as to where the incoming energy ends up in 3 dimensions. Not all watts are created equally, and where they are in the system is important.
The ocean is very different medium and surface to that of the land, and these differences are not sufficiently recognised.
On land, incoming energy is absorbed at the surface and conducted/convected/radiates from the surface. Therefore one might expect energy in to be balanced by energy out.
However, the ocean is different since it is a selective surface and one that is free to evaporate and with that process there is a change in latent energy..
DWLWIR is absorbed in the top few microns. Given the omnidirectional nature, virtually none makes it past about about 8 microns and more than 50% is absorbed in just 3 microns. There does not appear to be any process that can sequester the energy absorbed within the first few microns to depth thereby diluting and disipating it by volume, at a rate faster than the energy in the top few microns would drive evaporation.
Solar, of course, is very different since it is maily absorbed in the top few metres of the oceans (ie., in a volume a million times greater than that of DWLWIR and thereby is disluted by volume and gently warms the oceans, rather than driving evaporation. Some of it penetrates as far down as about 100 metres.
The important point to note is that the solar energy that is absorbed in the top few metres and not all of this energy finds its way to the surface. Due to mixing, the action of wind, waves, swell etc and ocean overturning some of the energy finds its way down to depth where it goes to warm the deep ocean, ie., warming the melt water from the Arctic/Antarctic in the thermohaline circulation.
The energy budget cartoon asssumes that the surface balances/should balance because it assumes that all incoming energy (solar and backrdiation) is absorbed at the surface and radiated/convected/conducted from the surface, but that is not the case.
Lord Monckton,
I think that Roy Spencer (http://wattsupwiththat.com/2015/06/27/i-only-ask-because-i-want-to-know/#comment-1973709) has given you the best response.
However, another answer is that you are free to define Lambda_0 any way you like (although some definitions might be more useful than others), but how you define it will depend on what the feedbacks end up being. Hence, you can’t redefine Lambda_0 to be in terms of the surface response and then use the feedbacks that were computed for the other definition.
As another example of this, Isaac Held has argued that it makes more sense to define Lambda_0 in a way such that the RELATIVE humidity, rather than the ABSOLUTE humidity, of the atmosphere is held constant. This leads to a “bare” climate sensitivity to CO2 doubling in the absence of feedbacks that is more like 2 C, rather than 1.2 C.
Using your logic, we would then conclude that if Held is “right”, then the climate sensitivity is more than 1.5 times as large as has been previously estimated. However, this is not correct (and is not what Held claims!!!) because the feedbacks are different if you define the “bare” sensitivity in this way. In particular, there is no longer a large water vapor feedback if your bare sensitivity is defined for the case that the RELATICE humidity remains constant.
joeldshore: Isaac Held has argued that it makes more sense to define Lambda_0 in a way such that the RELATIVE humidity, rather than the ABSOLUTE humidity, of the atmosphere is held constant.
Since neither is constant in the actual climate system, any derivation based on either assumption is inherently inaccurate by unknown amounts.
That is why Lambda_0 does NOT give the final estimate of climate sensitivity but only the 0th-order estimate.